A forest ranger in the west observation tower spots a fire 41° north of east. Fifteen miles directly east, the forest ranger in the east tower spots the same fire at 56° north of west. How far away is the ranger who is closest to the fire? Approximate the distance by rounding to the nearest hundredth of a mile.

The two sight lines and the 15-mile distance between towers form a triangle. Its angle at the fire is 180° − 41° − 56° = 83°. By the Law of Sines, the distance from the east tower is 15 sin(41°) ÷ sin(83°) ≈ 9.91 miles; this is shorter than the distance from the west tower. So the closest ranger is 9.91 miles away, choice A.

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